标题： 离散量子引力与量子场论 显示英文标题

标题： Discrete Quantum Gravity and Quantum Field Theory

摘要： 我们介绍了一个整数上的离散四维模，它似乎具有最大对称性。 通过附加通常的闵可夫斯基距离，我们得到了一个离散的四维闵可夫斯基空间。 在这个空间中构造宇宙历史并采用标准因果顺序，这些历史就变成了因果集。 这些因果集迅速增大，并描述了早期宇宙的暴胀时期。 接下来，我们考虑该模的对称群 $G$。 我们证明 $G$ 的阶为 24 并构建其群表。 在某种意义上，$G$ 是洛伦兹群的一个离散近似。 然而，我们注意到它不包含洛伦兹变换中的“boost”操作，本质上是一个旋转群。 构造了 $G$ 的酉表示。 得到了与离散模对偶的能量-动量空间，并推导出量子形式主义。 在这个结构上引入了一个离散的 Fock 空间，并研究了自由量子场。 最后，我们迈出了研究相互作用量子场的第一步。 显示英文摘要

摘要： We introduce a discrete 4-dimensional module over the integers that appears to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain a discrete 4-dimensional Minkowski space. Forming universe histories in this space and employing the standard causal order, the histories become causal sets. These causal sets increase in size rapidly and describe an inflationary period for the early universe. We next consider the symmetry group $G$ for the module. We show that $G$ has order 24 and we construct its group table. In a sense $G$ is a discrete approximation to the Lorentz group. However, we note that it contains no boosts and is essentially a rotation group. Unitary representations of $G$ are constructed. The energy-momentum space dual to the discrete module is obtained and a quantum formalism is derived. A discrete Fock space is introduced on this structure and free quantum fields are considered. Finally, we take the first step in a study of interacting quantum fields.